Fully populated VCM or the hidden parameter

Kermarrec, Gaël; Schön, Steffen

doi:10.1515/jogs-2017-0016

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…To that aim, we will investigate the extent to which the DCM proposed for GPS correlations together with a strictly linear functional model can be applied to the nonlinear problem of a plane fitting from TLS measurements. This new model was said, ironically, to account for correlations in an "hidden" way (Kermarrec and Schön 2017a). Up to now it has never been introduced, tested nor validated in engineering geodesy for nonlinear functional models.…”

Section: Introductionmentioning

confidence: 99%

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

Kermarrec

Lösler

2020

J Geod

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To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).

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Section: Introductionmentioning

confidence: 99%

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

Kermarrec

Lösler

2020

J Geod

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Efficient Approximation for a Fully Populated Variance-Covariance Matrix in RTK Positioning

Shen

2018

J. Surv. Eng.

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The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations: A proposal to account for correlations in least squares adjustment

Kermarrec

Neumann

Alkhatib

et al. 2019

Journal of Applied Geodesy

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The best unbiased estimates of unknown parameters in linear models have the smallest expected mean-squared errors as long as the residuals are weighted with their true variance–covariance matrix. As this condition is rarely met in real applications, the least-squares (LS) estimator is less trustworthy and the parameter precision is often overoptimistic, particularly when correlations are neglected. A careful description of the physical and mathematical relationships between the observations is, thus, necessary to reach a realistic solution and unbiased test statistics. Global Navigation Satellite Systems and terrestrial laser scanners (TLS) measurements show similarities and can be both processed in LS adjustments, either for positioning or deformation analysis. Thus, a parallel between stochastic models for Global Navigation Satellite Systems observations proposed previously in the case of correlations and functions for TLS range measurements based on intensity values can be drawn. This comparison paves the way for a simplified way to account for correlations for a use in LS adjustment.

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Fully populated VCM or the hidden parameter

Cited by 4 publications

References 25 publications

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

Efficient Approximation for a Fully Populated Variance-Covariance Matrix in RTK Positioning

The stochastic model for Global Navigation Satellite Systems and terrestrial laser scanning observations: A proposal to account for correlations in least squares adjustment

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